// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

/*

 * NOTE: This file is the modified version of xpivotL.c file in SuperLU

 * -- SuperLU routine (version 3.0) --
 * Univ. of California Berkeley, Xerox Palo Alto Research Center,
 * and Lawrence Berkeley National Lab.
 * October 15, 2003
 *
 * Copyright (c) 1994 by Xerox Corporation.  All rights reserved.
 *
 * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY
 * EXPRESSED OR IMPLIED.  ANY USE IS AT YOUR OWN RISK.
 *
 * Permission is hereby granted to use or copy this program for any
 * purpose, provided the above notices are retained on all copies.
 * Permission to modify the code and to distribute modified code is
 * granted, provided the above notices are retained, and a notice that
 * the code was modified is included with the above copyright notice.
 */
#ifndef SPARSELU_PIVOTL_H
#define SPARSELU_PIVOTL_H

namespace Eigen {
namespace internal {

/**
 * \brief Performs the numerical pivotin on the current column of L, and the CDIV operation.
 *
 * Pivot policy :
 * (1) Compute thresh = u * max_(i>=j) abs(A_ij);
 * (2) IF user specifies pivot row k and abs(A_kj) >= thresh THEN
 *           pivot row = k;
 *       ELSE IF abs(A_jj) >= thresh THEN
 *           pivot row = j;
 *       ELSE
 *           pivot row = m;
 *
 *   Note: If you absolutely want to use a given pivot order, then set u=0.0.
 *
 * \param jcol The current column of L
 * \param diagpivotthresh diagonal pivoting threshold
 * \param[in,out] perm_r Row permutation (threshold pivoting)
 * \param[in] iperm_c column permutation - used to finf diagonal of Pc*A*Pc'
 * \param[out] pivrow  The pivot row
 * \param glu Global LU data
 * \return 0 if success, i > 0 if U(i,i) is exactly zero
 *
 */
template<typename Scalar, typename StorageIndex>
Index
SparseLUImpl<Scalar, StorageIndex>::pivotL(const Index jcol,
										   const RealScalar& diagpivotthresh,
										   IndexVector& perm_r,
										   IndexVector& iperm_c,
										   Index& pivrow,
										   GlobalLU_t& glu)
{

	Index fsupc = (glu.xsup)((glu.supno)(jcol)); // First column in the supernode containing the column jcol
	Index nsupc = jcol - fsupc;	   // Number of columns in the supernode portion, excluding jcol; nsupc >=0
	Index lptr = glu.xlsub(fsupc); // pointer to the starting location of the row subscripts for this supernode portion
	Index nsupr = glu.xlsub(fsupc + 1) - lptr;					 // Number of rows in the supernode
	Index lda = glu.xlusup(fsupc + 1) - glu.xlusup(fsupc);		 // leading dimension
	Scalar* lu_sup_ptr = &(glu.lusup.data()[glu.xlusup(fsupc)]); // Start of the current supernode
	Scalar* lu_col_ptr = &(glu.lusup.data()[glu.xlusup(jcol)]);	 // Start of jcol in the supernode
	StorageIndex* lsub_ptr = &(glu.lsub.data()[lptr]);			 // Start of row indices of the supernode

	// Determine the largest abs numerical value for partial pivoting
	Index diagind = iperm_c(jcol); // diagonal index
	RealScalar pivmax(-1.0);
	Index pivptr = nsupc;
	Index diag = emptyIdxLU;
	RealScalar rtemp;
	Index isub, icol, itemp, k;
	for (isub = nsupc; isub < nsupr; ++isub) {
		using std::abs;
		rtemp = abs(lu_col_ptr[isub]);
		if (rtemp > pivmax) {
			pivmax = rtemp;
			pivptr = isub;
		}
		if (lsub_ptr[isub] == diagind)
			diag = isub;
	}

	// Test for singularity
	if (pivmax <= RealScalar(0.0)) {
		// if pivmax == -1, the column is structurally empty, otherwise it is only numerically zero
		pivrow = pivmax < RealScalar(0.0) ? diagind : lsub_ptr[pivptr];
		perm_r(pivrow) = StorageIndex(jcol);
		return (jcol + 1);
	}

	RealScalar thresh = diagpivotthresh * pivmax;

	// Choose appropriate pivotal element

	{
		// Test if the diagonal element can be used as a pivot (given the threshold value)
		if (diag >= 0) {
			// Diagonal element exists
			using std::abs;
			rtemp = abs(lu_col_ptr[diag]);
			if (rtemp != RealScalar(0.0) && rtemp >= thresh)
				pivptr = diag;
		}
		pivrow = lsub_ptr[pivptr];
	}

	// Record pivot row
	perm_r(pivrow) = StorageIndex(jcol);
	// Interchange row subscripts
	if (pivptr != nsupc) {
		std::swap(lsub_ptr[pivptr], lsub_ptr[nsupc]);
		// Interchange numerical values as well, for the two rows in the whole snode
		// such that L is indexed the same way as A
		for (icol = 0; icol <= nsupc; icol++) {
			itemp = pivptr + icol * lda;
			std::swap(lu_sup_ptr[itemp], lu_sup_ptr[nsupc + icol * lda]);
		}
	}
	// cdiv operations
	Scalar temp = Scalar(1.0) / lu_col_ptr[nsupc];
	for (k = nsupc + 1; k < nsupr; k++)
		lu_col_ptr[k] *= temp;
	return 0;
}

} // end namespace internal
} // end namespace Eigen

#endif // SPARSELU_PIVOTL_H
